RUI: Asymptotic and Numerical Techniques in Mathematical Modeling of Membrane Filtration

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Membrane filters – thin sheets of porous medium – find widespread use in applications such as water treatment, various purification processes in the biotech industry, removing impurities from the blood in kidney dialysis, beer clarification, and mask production, among many others. Membrane filters represent a multi-billion-dollar industry worldwide, and many major multinational companies maintain a keen interest in improving and optimizing the membrane filters they produce, in terms of both performance and cost. It is notable that the experimental literature far outweighs the theoretical and numerical; among the theoretical and numerical literature, there is a paucity of studies that offer first-principles, predictive mathematical models and simulations. This project aims to develop novel mathematical models with potential for significant impact in bridging this gap. The long-term goal is to improve and optimize membrane filters, in terms of both performance and cost. The project will involve students in the research.Filter performance depends strongly on key features of the porous membrane, including membrane thickness, internal pore structure and shape, pore connectivity, and variation of pore dimensions in the depth of the membrane. The complexity of the coupling between the membrane morphology, which evolves dynamically during the filtration process, and the details of the particle-laden flow, including possible stochastic behavior of the particles, make filtration and fouling a challenging predictive modeling problem. This project presents a coherent, first-principles approach to model both stochastic effects of particle dynamics and variations in internal membrane structure. The research aims to formulate and analyze novel mathematical models to investigate the evolution of membrane filters with complex internal structures by using asymptotic and numerical techniques. These models will be compared to observations, experiments, and data from industrial partners to understand more fully the co-evolution of membrane internal structure and flow in the context of porous media and membrane filters.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.